Your friend tells you he has a very simple trick for taking? one-third of the time it takes to repay your? mortgage: Use your Christmas bonus to make an extra payment on January 1 of each year? (that is, pay your monthly payment due on that day? twice). Assume that the mortgage has an original term of 30 years and has an APR of 12%.
a. If you take out your mortgage on January 1? (so that your first payment is due on February? 1), and you make your first extra payment at the end of the first? year, in what year will you finish repaying your? mortgage?
b. If you take out your mortgage on July 1? (so that the first payment is on August? 1), and you make the extra payment each? January, in how many months will you pay off your? mortgage?
c. How will the amount of time it takes to pay off the loan given this strategy vary with the interest rate on the? loan?